Problem: Solve for $x$ and $y$ using elimination. ${x-4y = -1}$ ${-4x+5y = -7}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $4$ ${4x-16y = -4}$ $-4x+5y = -7$ Add the top and bottom equations together. $-11y = -11$ $\dfrac{-11y}{{-11}} = \dfrac{-11}{{-11}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {x-4y = -1}\thinspace$ to find $x$ ${x - 4}{(1)}{= -1}$ $x-4 = -1$ $x-4{+4} = -1{+4}$ ${x = 3}$ You can also plug ${y = 1}$ into $\thinspace {-4x+5y = -7}\thinspace$ and get the same answer for $x$ : ${-4x + 5}{(1)}{= -7}$ ${x = 3}$